From very minor portions of dialogue, it can be assumed that his father started on a journey from Pallet Town much like Ash. Never formally introduced, the identity of his father has always been under heavy speculation. This speculated character however, have attained no hard evidence that they are in fact related to Ash in any way. In addition to that, during an interview with a storyboard artist for the Anime series, the artist stated that Ash's father is a man who is on his own Pokémon journey as a Trainer. Rumors say that Silver from the Pokémon Chronicles could be his father, with Giovanni and Professor Oak being equally thrown out by the fandom. In The Spell of the Unown the commentary version, the producer announced that more about him will be revealed in season 5, which eventually turned out to be untrue.
When Ash is recalling his past in DP138: Strategy Begins at Home!, a young man who appears to look similar to Ash and is petting a Rapidash, is shown, along with a young Ash. The Rapidash trainer's face was blurred, so his identity is unknown. The Rapidash trainer was indeed, Ash's father, but since his face was blurred, he could be anyone. It may be that he was a young Giovanni or Silver.